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Collective Model

Describes nuclear phenomena as arising from the collective motion of nucleons, incorporating concepts like vibrations and rotations.
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The statement of the theorem

The collective model describes the nuclear Hamiltonian H^coll\hat{H}_{coll} using collective coordinates, typically the quadrupole deformation parameters β\beta and γ\gamma. The Hamiltonian is generally written as: \nH^coll=12∑k=13(L^k22Ik+B^k22Bk)+V(β,γ)\hat{H}_{coll} = \frac{1}{2} \sum_{k=1}^{3} \left( \frac{\hat{L}_k^2}{2I_k} + \frac{\hat{B}_k^2}{2B_k} \right) + V(\beta, \gamma) \nwhere L^k\hat{L}_k and B^k\hat{B}_k are the angular momentum and vibrational operators, respectively. The potential V(β,γ)V(\beta, \gamma) is the potential energy surface governing the equilibrium deformation, often modeled by a polynomial expansion in β\beta and γ\gamma.